Rules · Structure · Walls · Doors & windows
In a bonded masonry wall the courses above an opening corbel over it of their own accord, so the lintel carries roughly the triangle of wall with sides rising at 60° from its ends; everything above that triangle arches onto the jambs.
load ≈ equilateral triangle on the span: W ≈ 0.43 · L² · t · ρ g
Every stone in a well-bonded wall overlaps the joints below it, so each course can step a little way out over a gap. Above a lintel the wall therefore behaves as if it were corbelled: the stones outside a steep triangle hang from their neighbours and pass their weight sideways to the jambs. Only the triangle of masonry inside that line bears on the lintel. Builders’ rules of thumb since the Middle Ages take this triangle as equilateral.
The Mycenaeans made the principle explicit by leaving the triangle empty (the relieving triangle), and later builders achieved the same end with a discharging arch built into the wall over a flat lintel.
In a corbelled vault each course may project only a little beyond the one below, and each overhanging half must have its centre of gravity behind the inner face of its wall; load the tails of the stones with heavy hearting until the capstone is set.
stable if Σ W·x (behind the springing edge) > Σ W·x (in front)
A beam is squeezed along its top and stretched along its bottom; stone resists squeezing well but stretching badly, so a stone lintel must be deep in proportion to its span and cannot be long. Doubling the span quadruples the stress from its own weight.
σ ≈ ¾ ρ g L² ⁄ d (self-weight) · + ≈ 0.43 ρ g L³ ⁄ d² (a wall above)
Weight for weight, timber is many times stronger in bending than stone; long spans in trabeated buildings are therefore roofed with timber beams resting on stone walls and columns.
bending strength ÷ density: oak ≈ 70 · limestone ≈ 3 (kPa per kg ⁄ m³)
The royal tomb grew in about a century from a low battered mastaba, through a stack of diminishing mastabas (the step pyramid), to a smooth-faced true pyramid; a failure of stability in between forced the change of slope of the Bent Pyramid.
When a steep pyramid shows signs of distress, flatten the slope of the upper part: Sneferu’s pyramid at Dahshur rises at about 54° for its lower part and about 43° above.
lower seked 5 palms (≈ 54.5°) → upper ≈ 7½ palms (≈ 43°)
Make the outer faces of pylons, enclosure walls and mastabas lean inward as they rise, so that the wall is thickest at its foot; mark the corners with a torus roll.
batter of pylons ≈ 1 : 8 (about 83°)
Cite this page Chris Paton, “A lintel carries only a triangle of the wall above it”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/lintel-load-triangle. Text, drawings and models licensed under CC BY-NC 4.0.